This invention relates to spatial light modulators, and more particularly to a method of mapping between diagonal pixel control patterns and rectangular pixel control patterns.
A Digital Micromirror Device(trademark) (DMD(trademark)) is a type of microelectromechanical systems (MEMS) device. Invented in 1987 at Texas Instruments Incorporated, the DMD is a fast, reflective digital spatial light modulator. It can be combined with image processing, memory, a light source, and optics to form a digital light processing system capable of projecting large, bright, high-contrast color images. It may also be used for other applications, such as for optical switching and in optical equalization systems.
The DMD is fabricated using CMOS-like processes over a CMOS memory. It has an array of individually addressable mirror elements, each having an aluminum mirror that can reflect light in one of two directions depending on the state of an underlying memory cell. With the memory cell in a first state, the mirror rotates to +10 degrees. With the memory cell in a second state, the mirror rotates to xe2x88x9210 degrees. When the mirror surfaces are illuminated with a light source, the mirrors in the array can be set to one state or the other, such that xe2x80x9conxe2x80x9d mirrors reflect light to one location and xe2x80x9coffxe2x80x9d mirrors reflect light to another location.
This on or off capability of the mirror elements has led to numerous applications for DMDs. For imaging applications, the xe2x80x9conxe2x80x9d mirror elements reflect light to an image plane. For optical switching applications, the mirror positions can be used to direct a beam of light to a given output path. Another application is for optical equalization, where input wavelengths are directed to different portions of the DMD array, and each wavelength is selectively attenuated so that the outputs are equalized.
The DMD architecture is such that the rotation of each mirror element is along the diagonal of the mirror. Because of this, the mirror surfaces are illuminated along their diagonals.
Thus, when the DMD is used for optical equalization, the input signal illuminates the DMD mirror surfaces along the mirror diagonals. As a result, pixel control patterns are along diagonal paths. This requires the control values to be mapped to the rectangular control architecture of the DMD pixel array.
One aspect of the invention is a method of using a spatial light modulator (SLM) to control the gain of an input optical signal. The gain control achieved by determining a two-dimensional grid of values, each value representing an on or off position of pixel elements of the SLM. A is u,v space is defined for the diagonal rows and columns, such that the u axis and v axis run through diagonals of each grid element. Each grid element is assigned a u,v coordinate pair. For each grid element in the u,v space, an x,y coordinate pair is calculated by performing the following operation:       [                            x                                      y                      ]    =      int    ⁢          xe2x80x83        ⁢          (                                    [                                                            0.5                                                  1                                                                                                  -                    0.5                                                                    1                                                      ]                    ·                      [                                                            u                                                                              v                                                      ]                          +                  [                                                    0.5                                                                    0.5                                              ]                    )      
Each non-integer value is then rounded to an adjacent pixel value. For example, the next smallest integer value, int(8.5)=8 and int (xe2x88x929.5)=xe2x88x9210.
An advantage of the invention is that it provides a means to describe pixel control values in diagonal pixel space, then translate the results onto the rectangular space of the SLM. The conventional alternative is to work in rectangular space, then use complex mathematical operations to rotate pixel control values.